0,0 → 1,365 |
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/* @(#)fdlibm.h 5.1 93/09/24 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* Developed at SunPro, a Sun Microsystems, Inc. business. |
* Permission to use, copy, modify, and distribute this |
* software is freely granted, provided that this notice |
* is preserved. |
* ==================================================== |
*/ |
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/* REDHAT LOCAL: Include files. */ |
#include <math.h> |
#include <sys/types.h> |
#include <machine/ieeefp.h> |
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/* REDHAT LOCAL: Default to XOPEN_MODE. */ |
#define _XOPEN_MODE |
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/* Most routines need to check whether a float is finite, infinite, or not a |
number, and many need to know whether the result of an operation will |
overflow. These conditions depend on whether the largest exponent is |
used for NaNs & infinities, or whether it's used for finite numbers. The |
macros below wrap up that kind of information: |
|
FLT_UWORD_IS_FINITE(X) |
True if a positive float with bitmask X is finite. |
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FLT_UWORD_IS_NAN(X) |
True if a positive float with bitmask X is not a number. |
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FLT_UWORD_IS_INFINITE(X) |
True if a positive float with bitmask X is +infinity. |
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FLT_UWORD_MAX |
The bitmask of FLT_MAX. |
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FLT_UWORD_HALF_MAX |
The bitmask of FLT_MAX/2. |
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FLT_UWORD_EXP_MAX |
The bitmask of the largest finite exponent (129 if the largest |
exponent is used for finite numbers, 128 otherwise). |
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FLT_UWORD_LOG_MAX |
The bitmask of log(FLT_MAX), rounded down. This value is the largest |
input that can be passed to exp() without producing overflow. |
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FLT_UWORD_LOG_2MAX |
The bitmask of log(2*FLT_MAX), rounded down. This value is the |
largest input than can be passed to cosh() without producing |
overflow. |
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FLT_LARGEST_EXP |
The largest biased exponent that can be used for finite numbers |
(255 if the largest exponent is used for finite numbers, 254 |
otherwise) */ |
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#ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL |
#define FLT_UWORD_IS_FINITE(x) 1 |
#define FLT_UWORD_IS_NAN(x) 0 |
#define FLT_UWORD_IS_INFINITE(x) 0 |
#define FLT_UWORD_MAX 0x7fffffff |
#define FLT_UWORD_EXP_MAX 0x43010000 |
#define FLT_UWORD_LOG_MAX 0x42b2d4fc |
#define FLT_UWORD_LOG_2MAX 0x42b437e0 |
#define HUGE ((float)0X1.FFFFFEP128) |
#else |
#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L) |
#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L) |
#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L) |
#define FLT_UWORD_MAX 0x7f7fffffL |
#define FLT_UWORD_EXP_MAX 0x43000000 |
#define FLT_UWORD_LOG_MAX 0x42b17217 |
#define FLT_UWORD_LOG_2MAX 0x42b2d4fc |
#define HUGE ((float)3.40282346638528860e+38) |
#endif |
#define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23)) |
#define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23) |
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/* Many routines check for zero and subnormal numbers. Such things depend |
on whether the target supports denormals or not: |
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FLT_UWORD_IS_ZERO(X) |
True if a positive float with bitmask X is +0. Without denormals, |
any float with a zero exponent is a +0 representation. With |
denormals, the only +0 representation is a 0 bitmask. |
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FLT_UWORD_IS_SUBNORMAL(X) |
True if a non-zero positive float with bitmask X is subnormal. |
(Routines should check for zeros first.) |
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FLT_UWORD_MIN |
The bitmask of the smallest float above +0. Call this number |
REAL_FLT_MIN... |
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FLT_UWORD_EXP_MIN |
The bitmask of the float representation of REAL_FLT_MIN's exponent. |
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FLT_UWORD_LOG_MIN |
The bitmask of |log(REAL_FLT_MIN)|, rounding down. |
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FLT_SMALLEST_EXP |
REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported, |
-22 if they are). |
*/ |
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#ifdef _FLT_NO_DENORMALS |
#define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L) |
#define FLT_UWORD_IS_SUBNORMAL(x) 0 |
#define FLT_UWORD_MIN 0x00800000 |
#define FLT_UWORD_EXP_MIN 0x42fc0000 |
#define FLT_UWORD_LOG_MIN 0x42aeac50 |
#define FLT_SMALLEST_EXP 1 |
#else |
#define FLT_UWORD_IS_ZERO(x) ((x)==0) |
#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L) |
#define FLT_UWORD_MIN 0x00000001 |
#define FLT_UWORD_EXP_MIN 0x43160000 |
#define FLT_UWORD_LOG_MIN 0x42cff1b5 |
#define FLT_SMALLEST_EXP -22 |
#endif |
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#ifdef __STDC__ |
#undef __P |
#define __P(p) p |
#else |
#define __P(p) () |
#endif |
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/* |
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h> |
* (one may replace the following line by "#include <values.h>") |
*/ |
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#define X_TLOSS 1.41484755040568800000e+16 |
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/* Functions that are not documented, and are not in <math.h>. */ |
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extern double logb __P((double)); |
#ifdef _SCALB_INT |
extern double scalb __P((double, int)); |
#else |
extern double scalb __P((double, double)); |
#endif |
extern double significand __P((double)); |
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/* ieee style elementary functions */ |
extern double __ieee754_sqrt __P((double)); |
extern double __ieee754_acos __P((double)); |
extern double __ieee754_acosh __P((double)); |
extern double __ieee754_log __P((double)); |
extern double __ieee754_atanh __P((double)); |
extern double __ieee754_asin __P((double)); |
extern double __ieee754_atan2 __P((double,double)); |
extern double __ieee754_exp __P((double)); |
extern double __ieee754_cosh __P((double)); |
extern double __ieee754_fmod __P((double,double)); |
extern double __ieee754_pow __P((double,double)); |
extern double __ieee754_lgamma_r __P((double,int *)); |
extern double __ieee754_gamma_r __P((double,int *)); |
extern double __ieee754_log10 __P((double)); |
extern double __ieee754_sinh __P((double)); |
extern double __ieee754_hypot __P((double,double)); |
extern double __ieee754_j0 __P((double)); |
extern double __ieee754_j1 __P((double)); |
extern double __ieee754_y0 __P((double)); |
extern double __ieee754_y1 __P((double)); |
extern double __ieee754_jn __P((int,double)); |
extern double __ieee754_yn __P((int,double)); |
extern double __ieee754_remainder __P((double,double)); |
extern __int32_t __ieee754_rem_pio2 __P((double,double*)); |
#ifdef _SCALB_INT |
extern double __ieee754_scalb __P((double,int)); |
#else |
extern double __ieee754_scalb __P((double,double)); |
#endif |
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/* fdlibm kernel function */ |
extern double __kernel_standard __P((double,double,int)); |
extern double __kernel_sin __P((double,double,int)); |
extern double __kernel_cos __P((double,double)); |
extern double __kernel_tan __P((double,double,int)); |
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const __int32_t*)); |
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/* Undocumented float functions. */ |
extern float logbf __P((float)); |
#ifdef _SCALB_INT |
extern float scalbf __P((float, int)); |
#else |
extern float scalbf __P((float, float)); |
#endif |
extern float significandf __P((float)); |
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/* ieee style elementary float functions */ |
extern float __ieee754_sqrtf __P((float)); |
extern float __ieee754_acosf __P((float)); |
extern float __ieee754_acoshf __P((float)); |
extern float __ieee754_logf __P((float)); |
extern float __ieee754_atanhf __P((float)); |
extern float __ieee754_asinf __P((float)); |
extern float __ieee754_atan2f __P((float,float)); |
extern float __ieee754_expf __P((float)); |
extern float __ieee754_coshf __P((float)); |
extern float __ieee754_fmodf __P((float,float)); |
extern float __ieee754_powf __P((float,float)); |
extern float __ieee754_lgammaf_r __P((float,int *)); |
extern float __ieee754_gammaf_r __P((float,int *)); |
extern float __ieee754_log10f __P((float)); |
extern float __ieee754_sinhf __P((float)); |
extern float __ieee754_hypotf __P((float,float)); |
extern float __ieee754_j0f __P((float)); |
extern float __ieee754_j1f __P((float)); |
extern float __ieee754_y0f __P((float)); |
extern float __ieee754_y1f __P((float)); |
extern float __ieee754_jnf __P((int,float)); |
extern float __ieee754_ynf __P((int,float)); |
extern float __ieee754_remainderf __P((float,float)); |
extern __int32_t __ieee754_rem_pio2f __P((float,float*)); |
#ifdef _SCALB_INT |
extern float __ieee754_scalbf __P((float,int)); |
#else |
extern float __ieee754_scalbf __P((float,float)); |
#endif |
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/* float versions of fdlibm kernel functions */ |
extern float __kernel_sinf __P((float,float,int)); |
extern float __kernel_cosf __P((float,float)); |
extern float __kernel_tanf __P((float,float,int)); |
extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*)); |
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/* The original code used statements like |
n0 = ((*(int*)&one)>>29)^1; * index of high word * |
ix0 = *(n0+(int*)&x); * high word of x * |
ix1 = *((1-n0)+(int*)&x); * low word of x * |
to dig two 32 bit words out of the 64 bit IEEE floating point |
value. That is non-ANSI, and, moreover, the gcc instruction |
scheduler gets it wrong. We instead use the following macros. |
Unlike the original code, we determine the endianness at compile |
time, not at run time; I don't see much benefit to selecting |
endianness at run time. */ |
|
#ifndef __IEEE_BIG_ENDIAN |
#ifndef __IEEE_LITTLE_ENDIAN |
#error Must define endianness |
#endif |
#endif |
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/* A union which permits us to convert between a double and two 32 bit |
ints. */ |
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#ifdef __IEEE_BIG_ENDIAN |
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typedef union |
{ |
double value; |
struct |
{ |
__uint32_t msw; |
__uint32_t lsw; |
} parts; |
} ieee_double_shape_type; |
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#endif |
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#ifdef __IEEE_LITTLE_ENDIAN |
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typedef union |
{ |
double value; |
struct |
{ |
__uint32_t lsw; |
__uint32_t msw; |
} parts; |
} ieee_double_shape_type; |
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#endif |
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/* Get two 32 bit ints from a double. */ |
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#define EXTRACT_WORDS(ix0,ix1,d) \ |
do { \ |
ieee_double_shape_type ew_u; \ |
ew_u.value = (d); \ |
(ix0) = ew_u.parts.msw; \ |
(ix1) = ew_u.parts.lsw; \ |
} while (0) |
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/* Get the more significant 32 bit int from a double. */ |
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#define GET_HIGH_WORD(i,d) \ |
do { \ |
ieee_double_shape_type gh_u; \ |
gh_u.value = (d); \ |
(i) = gh_u.parts.msw; \ |
} while (0) |
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/* Get the less significant 32 bit int from a double. */ |
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#define GET_LOW_WORD(i,d) \ |
do { \ |
ieee_double_shape_type gl_u; \ |
gl_u.value = (d); \ |
(i) = gl_u.parts.lsw; \ |
} while (0) |
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/* Set a double from two 32 bit ints. */ |
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#define INSERT_WORDS(d,ix0,ix1) \ |
do { \ |
ieee_double_shape_type iw_u; \ |
iw_u.parts.msw = (ix0); \ |
iw_u.parts.lsw = (ix1); \ |
(d) = iw_u.value; \ |
} while (0) |
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/* Set the more significant 32 bits of a double from an int. */ |
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#define SET_HIGH_WORD(d,v) \ |
do { \ |
ieee_double_shape_type sh_u; \ |
sh_u.value = (d); \ |
sh_u.parts.msw = (v); \ |
(d) = sh_u.value; \ |
} while (0) |
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/* Set the less significant 32 bits of a double from an int. */ |
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#define SET_LOW_WORD(d,v) \ |
do { \ |
ieee_double_shape_type sl_u; \ |
sl_u.value = (d); \ |
sl_u.parts.lsw = (v); \ |
(d) = sl_u.value; \ |
} while (0) |
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/* A union which permits us to convert between a float and a 32 bit |
int. */ |
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typedef union |
{ |
float value; |
__uint32_t word; |
} ieee_float_shape_type; |
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/* Get a 32 bit int from a float. */ |
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#define GET_FLOAT_WORD(i,d) \ |
do { \ |
ieee_float_shape_type gf_u; \ |
gf_u.value = (d); \ |
(i) = gf_u.word; \ |
} while (0) |
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/* Set a float from a 32 bit int. */ |
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#define SET_FLOAT_WORD(d,i) \ |
do { \ |
ieee_float_shape_type sf_u; \ |
sf_u.word = (i); \ |
(d) = sf_u.value; \ |
} while (0) |